Math Monday: Fold Your Own Hyperbolic Paraboloids

by George Hart

By pleating a square sheet of paper with a pattern of concentric squares, one can fold a saddle shape that mathematicians call a hyperbolic paraboloid, sometimes nicknamed a hypar. Erik Demaine led a workshop at a recent Museum of Mathematics event where he showed how multiple hypars can be assembled to make star-like geometric forms. During the Math Encounters presentation, fifty people folded hypars and joined them to make this construction.There are twenty four sheets all together, arranged as a group of four for each face of an imagined cube. Erik’s paper about the mathematical ideas and detailed folding instructions to make your own pleated hypars are available on his web site, here.